0
votes
2answers
67 views

What is difference between Fourier Transform and Fast Fourier Transform?

If you think about Fourier Transform, in the classical cases, say on the real line, what it is? Just a waded sum. Right? You take a function $f$, and you take it's Fourier Transform at particular ...
0
votes
1answer
34 views

Is there an equivalent of Plancherel's theorem with wavelets transform?

For the Fourier transform, we know that: $$||f||_2=c||\hat{f}||_2$$ where $c$ depends on the normalization. Is there an equivalent with wavelet transform? Thanks.
1
vote
1answer
59 views

Wavelet or FFT for Transient signal analysis?

For now I use FFT to analyze the response of an electrical system to some transient signal. The transient signal is $x(t)$, which translates to $X(w)$ in the frenquency domain. On the other hand I ...
0
votes
1answer
36 views

Amplitude Spectrum, Nyquist Frequency, mixed/min/max wavelets

The problem is here. Now I know the definition of mixed/max/min phase wavelets, whether the roots lie within the unit circle or not. Starting from n = 1, let $$ x_t = ( 5, 6) $$ $$ X(z) = 5 + 6z $$ ...
0
votes
0answers
23 views

Evaluating an integral involving Haar scaling function

Let $\phi(t)$ denote the Haar scaling function, and let $\psi(t)$ be the corresponding wavelet. My problem is to evaluate the integral $I = \int_{t} \phi(t - 1/2) \frac{\partial \psi(t)}{\partial t} ...
2
votes
2answers
61 views

In which case should a wavelet transform be applied instead of a Fourier transform?

I was wondering what are the advantages (and possibly the drawbacks) of using a wavelet transform instead of a Fourier transform for the signal processing, are there simple examples to illustrate that ...
2
votes
1answer
103 views

Need to learn wavelet, suggest steps and resources

I am looking for a good introduction to wavelets and wavelet transforms. that covers the following: Basics Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality and ...
1
vote
1answer
73 views

Denoise using wavelet transform

My mathematical class task is to de-noise a function using wavelet transform. I am to select a function $f(x)$ and noise function with zero-mean $n(x)$. I am to add noise like this: $$f_{noise}(x) = ...
2
votes
1answer
64 views

Daubechies wavelet

I have two question about Daubechies wavelet are they really orthogonality? for example daub4 has the support equal $[0-3]$, and for scale function we have must: $$ \int_0^3\phi(x-n)*\phi(x-m)dx ...
2
votes
2answers
148 views

Morlet's wavelet reconstruction formula

The CWT (continuous wavelet transform) of a signal $x(t)$ is $$X_w(a,b)=\frac{1}{\sqrt{|a|}} \int_{-\infty}^{\infty} x(t)\psi^{\ast}\left(\frac{t-b}{a}\right)\, dt$$ In order to reconstruct the ...
2
votes
1answer
148 views

compare wavelet and Fourier transform

i would like to compare each other wavelet and Fourier transform on given signal,let us consider following signal ...
1
vote
0answers
67 views

Output of wavelet transforms

I am working on a time sensitive computer science and fluid dynamics project that requires me to find applications of wavelet analysis. I know that at its core, a wavelet transform simply takes a ...
2
votes
0answers
117 views

An exercise. A property of the Fourier transform of wavelet

In the book "An Introduction To Wavelet Analysis" by David F. Walnut, there is, Exercise 7.45. Show that if $\psi(x)$ is a wavelet, then $\sum\limits_{j}{\left|\hat{\psi}(2^j\gamma)\right|^2} = 1$ ...
3
votes
1answer
239 views

A theorem about Lipschitz regularity and Fourier transform

How to prove that: A function $f$ is uniformly Lipschitz $\alpha$ over $\mathbb R$ if $$\int_{-\infty}^{+\infty}|\hat f(\omega)|(1+|\omega|^\alpha)d\omega<+\infty$$ A function $f$ is uniformly ...
13
votes
4answers
6k views

Difference between Fourier transform and Wavelets

While understanding difference between wavelets and Fourier transform I came across this point in Wikipedia. The main difference is that wavelets are localized in both time and frequency whereas ...
0
votes
0answers
115 views

Wavelet Transforms

I don't know as much as I would like to about Fourier analysis and I know almost nothing about wavelets. So just have a few conceptual questions to determine whether I should pursue their study or ...
0
votes
2answers
2k views

DFT and DWT difference?

what is the basic difference between the Discrete Fourier Transform and the Wavelet Transform ? and why does JPEG2000 preferred DWT over DCT or DFT ?
2
votes
1answer
134 views

Best way to find magnitude and phase of a specific frequency in an empirical time series…

I've a discrete, univariate time series, and I'm interested in to investigate a specific frequency component. Assume I'm interested in a frequency with a cycle-time of $f$ samples - and I need to get ...
5
votes
1answer
497 views

Wavelet Theory — where do I start?

I am in the process of implementing a Fixed-Point Fast Fourier Transform. The Fixed-Point FFT requires mathematical background in the area of wavelets and lifting schemes. What are good ...
7
votes
3answers
616 views

Decomposing a discrete signal into a sum of rectangle functions

Hello math@stackexchange community ! I have a simple question that seems to have a non trivial answer. Given a discrete one dimensional signal $w(x)$ defined in a finite range, and the boxcar ...
5
votes
2answers
485 views

Which time-frequency coefficients does the Wavelet transform compute?

(I asked this on Stack Overflow a while ago and didn't get a satisfying answer, so I'm trying again here.) The Fast Fourier Transform takes O(N log N) operations, while the Fast Wavelet Transform ...